Five Secret Shares

Five sailors have gathered a pile of coconuts, watched by a monkey. During the night, the first sailor wakes and divides the pile into five equal shares. One coconut is left over, so he gives it to the monkey. He hides one share for himself, recombines the other four shares, and goes back to sleep. Later, each of the other four sailors independently does exactly the same thing, always finding that the pile leaves precisely one coconut after division by five. None knows what the others have done. In the morning, the sailors divide the remaining pile into five equal shares, this time with no coconut left over. What is the smallest possible number of coconuts in the original pile?